No, it is not true.

With a US passport, your movements will be recorded with passport stamps. Some citizens may use ID cards and their movements are not recorded.

So it depends on how you entered Kosovo. If you entered Serbia initially and then go to Kosovo, you can go back to Serbia. This is because from the Serbian perspective, where Kosovo is part of Serbia, you are still in the same country (and your 90-day stay limit continues from your original entry into Serbia).

If you entered Kosovo from any other country, from the Serbian perspective you actually entered Serbia, but at an illegal border crossing, so your presence in Serbia is unauthorized. Thus, they won't permit you to pass into the part of Serbian territory under Serbian control.

With a car, it gets more complicated if you have Serbian or Kosovar plates. If it's registered in a third country it should be OK provided you entered Serbia properly (according to Serbia), but if a rental you should make sure they allow you to drive into both Kosovo and Serbia. AFAIK, you should be able to use the Merdare border crossing to return to Serbia provided your entry into Kosovo was from Serbia.